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Zélus: A synchronous language with ODEs


Timothy Bourke and Marc Pouzet



Ecole normale supérieure

University of Pierre & Marie Curie


Zélus is a new programming language for modeling systems that mix discrete logical time and continuous time behaviors. From a user's perspective, its main originality is to extend an existing Lustre-like synchronous language with Ordinary Differential Equations (ODEs). The extension is conservative: any synchronous program expressed as data-flow equations and hierarchical automata can be composed arbitrarily with ODEs in the same source code.

A dedicated type system and causality analysis ensure that all discrete changes are aligned with zero-crossing events so that no side effects or discontinuities occur during integration. Programs are statically scheduled and translated into sequential code that, by construction, runs in bounded time and space. Compilation is effected by source-to-source translation into a small synchronous subset which is processed by a standard synchronous compiler architecture. The resultant code is paired with an off-the-shelf numeric solver.

We show that it is possible to build a modeler for explicit hybrid systems à la Simulink/Stateflow on top of an existing synchronous language, using it both as a semantic basis and as a target for code generation.

BibTeX Entry

    publisher        = {ACM},
    author           = {Bourke, Timothy and Pouzet, Marc},
    month            = apr,
    editor           = {{Calin Belta and Franjo Ivancic}},
    year             = {2013},
    keywords         = {zélus; hybrid systems; hybrid automata; synchronous languages; block diagrams; type systems},
    title            = {Zélus: A Synchronous Language with {ODEs}},
    booktitle        = {Hybrid Systems: Computation and Control},
    pages            = {113-118},
    address          = {Philadelphia, USA}


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